Re: Constitution, Miranda, and Constelation Class
The only true "fingerprint" ships in the Trekverse ever seem to give is their warp signature, which can be read through cloaking devices, holographic overpainting, attempts at broadcasting a false signature over the top of it etc
Which is useless if the warp drive is disengaged, such as the crippled Stargazer.
"But there's no sense crying over every mistake. You just keep on trying till you run out of cake."